Yu.Burman
Geometry of manifolds and bundles
Course synopsis
- Riemannian metrics. Curvature. Gauss--Bonnet formula.
- Covariant differentiation. Connections on a linear bundle --- various definitions and equivalence.
- Frobenius theorem.
- Euler class of a linear bundle.
- Levi--Civita connection.
- Symplectic structures and Poisson brackets. Symplectic leaves. Symplecticity of the geodesic flow.